Question

question
find the distance between the two points in simplest radical form.
(-8, -3) and (-1, 4)

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-8,y_1 = - 3,x_2=-1,y_2 = 4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=-1-(-8)=-1 + 8=7$.
$y_2 - y_1=4-(-3)=4 + 3=7$.

Step3: Substitute into formula

Substitute the values into the distance formula:
$d=\sqrt{(7)^2+(7)^2}=\sqrt{49 + 49}=\sqrt{98}$.

Step4: Simplify radical

Simplify $\sqrt{98}$: $\sqrt{98}=\sqrt{49\times2}=\sqrt{49}\times\sqrt{2}=7\sqrt{2}$.

Answer:

$7\sqrt{2}$